Omg, you have to learn to express yourself clearly, what you seem to mean is that while some of the difference between the performances of men and women in chess may be due to priming, priming may not explain all of that difference. Fair enough, but you did not bring any proof of that, so I can only assume you base your assertion merely on your own prejudices. As for me, I could as well say that without priming, women would be better than men at chess.

I am not suggesting that I can prove (with argument,(no one can)) that nature topples nurture .. I am on the other hand suggesting that this study (like so many like it) is inconclusive, that the method makes the data inconclusive.

And I don't need to prove that both are at work to a varying degree... the science on that is self-evident to anyone who knows the field.

To me, the data is conclusive in so far as it proves what the authors say it proves. They don't say what you seem to think they say; although another commenter did provides some interesting calculations of how much higher ratings women would have in the absence of stereotype threat, which goes towards quantifying nature vs. nurture.

No science is ever self-evident to one who really knows the field. And making a statement in science bears the burden of proof.